Risk allocation helps add alpha in good times and bad

Risk capital allocation has received little attention in discussions about asset allocation, in spite of its importance to investment performance. Its relationship to performance can be seen first through a qualitative lens, and then through a quantitative one by using the Mahalanobis distance, a concept first introduced by Mark Kritzman in an article he wrote with Yuanzhen Li, “Skulls, Financial Turbulence, and Risk Management” (see Financial Analysts Journal, vol. 66, no. 5).

From a qualitative standpoint, if looking back at the period of low volatility from 2005 to 2006, investors sought to fulfill a fixed risk budget and were forced to increase exposure to assets that had little historical volatility. Many fixed income managers bought riskier positions, such as credit default obligations (CDOs) or non-conforming mortgage-backed securities (MBSs). Then, in 2008, as markets dislocated, volatilities spiked and spreads widened indiscriminately across credit sensitive securities, the reward for holding such credit-sensitive investments improved markedly. However, investors working with a fixed risk budget were forced to offload such securities at heavily discounted prices.

For investment managers, the definition of good times and bad times depends on our ability to seize investment opportunities — the opportunity set — in a given risk environment. When the opportunity set is large, we see mispricing that can be exploited and we take risk. However, when the opportunity is small, there is little mispricing and we reduce risk. Unless we face the exact same opportunity set in each period, we need to pay attention to managing and allocating this risk budget across multiple horizons because this process creates risk in and of itself. This is known as endogenous risk.

Quantitative lens

From a quantitative standpoint, if we want to reach a certain risk budget over time, then we need to allocate risk across different periods. Variations through time in an asset’s expected excess returns and expected covariance matrix imply changes in the level and shape of the efficient frontier and, thus, changes in the opportunity set and risk environment that investors face with the asset.

The risk one should take in each period is directly and linearly related to the expected Sharpe ratio of the portfolio. When the Sharpe ratio is low, we want to take less risk. When the Sharpe ratio is high, we want to take more risk, making the ex-ante Sharpe ratio a perfect measure to assess exactly how much risk we should take. The Sharpe ratio corresponds to the Mahalanobis distance of the alphas. Using Mahalanobis distance allows us to understand how investment opportunities are created at security level and how those opportunities aggregate at the strategy level, taking into account both volatility and correlations.

Take the MSCI U.S. and Canada, for example. These are two highly correlated markets, so a large expected return in one market coupled with a small or negative expected return in the other creates a large investment opportunity, because an investor can go long one market and short the other. This keeps the risk low and expected return high.

If investors can decompose the source of the opportunities to get a general sense of how much value-add comes from variations in the opportunity set and the level of the opportunity set, they will see that 80% of alpha has come from allocation across assets and 20% has come from allocation across periods. In order for risk allocation across periods to work, it is of course a prerequisite that allocation across asset classes works. One can’t leverage negative alpha with time allocation, but one can enhance an asset allocation strategy that adds value by deploying risk capital wisely across investment periods.